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Particle swarm optimization (PSO) has witnessed giant success in problem optimization. Nevertheless, its optimization performance seriously degrades when coping with optimization problems with a lot of local optima. To alleviate this issue, this paper designs a predominant cognitive learning particle swarm optimization (PCLPSO) method to effectively tackle complicated optimization problems. Specifically, for each particle, a new promising exemplar is constructed by letting its personal best position cognitively learn from a better personal experience randomly selected from those of others based on a novel predominant cognitive learning strategy. As a result, different particles preserve different guiding exemplars. In this way, the learning effectiveness and the learning diversity of particles are expectedly improved. To eliminate the dilemma that PCLPSO is sensitive to the involved parameters, we propose dynamic adjustment strategies, so that different particles preserve different parameter settings, which is further beneficial to promote the learning diversity of particles. With the above techniques, the proposed PCLPSO could expectedly compromise the search intensification and diversification in a good way to search the complex solution space properly to achieve satisfactory performance. Comprehensive experiments are conducted on the commonly adopted CEC 2017 benchmark function set to testify the effectiveness of the devised PCLPSO. Experimental results show that PCLPSO obtains considerably competitive or even much more promising performance than several representative and state-of-the-art peer methods. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) has exhibited well-known feasibility in problem optimization. However, its optimization performance still encounters challenges when confronted with complicated optimization problems with many local areas. In PSO, the interaction among particles and utilization of the communication information play crucial roles in improving the learning effectiveness and learning diversity of particles. To promote the communication effectiveness among particles, this paper proposes a stochastic triad topology to allow each particle to communicate with two random ones in the swarm via their personal best positions. Then, unlike existing studies that employ the personal best positions of the updated particle and the neighboring best position of the topology to direct its update, this paper adopts the best one and the mean position of the three personal best positions in the associated triad topology as the two guiding exemplars to direct the update of each particle. To further promote the interaction diversity among particles, an archive is maintained to store the obsolete personal best positions of particles and is then used to interact with particles in the triad topology. To enhance the chance of escaping from local regions, a random restart strategy is probabilistically triggered to introduce initialized solutions to the archive. To alleviate sensitivity to parameters, dynamic adjustment strategies are designed to dynamically adjust the associated parameter settings during the evolution. Integrating the above mechanism, a stochastic triad topology-based PSO (STTPSO) is developed to effectively search complex solution space. With the above techniques, the learning diversity and learning effectiveness of particles are largely promoted and thus the developed STTPSO is expected to explore and exploit the solution space appropriately to find high-quality solutions. Extensive experiments conducted on the commonly used CEC 2017 benchmark problem set with different dimension sizes substantiate that the proposed STTPSO achieves highly competitive or even much better performance than state-of-the-art and representative PSO variants. [ABSTRACT FROM AUTHOR]

As optimization problems become more and more complex in real-world scenarios, the effectiveness of many existing differential evolution (DE) methods is critically challenged. To circumvent this predicament, this paper proposes a triple competitive DE (TCDE) to tackle increasingly complicated optimization problems. Specifically, a triple competition mechanism is devised to first randomly arrange individuals into exclusive triples and then let individuals in each triple compete with each other. Subsequently, heterogeneous mutation schemes are designed to update the three individuals in each triple based on the competition results. With the cooperation between these two techniques, on the one hand, better individuals in the triples tend to exploit the areas where they lie to find high-accuracy solutions, while worse individuals in the triples prefer to explore the intricate problem space to locate promising regions. On the other hand, different individuals are mutated by following the guidance of different leading exemplars, which ensures that individuals traverse the sophisticated solution space in diverse directions along with slight intensification to optimal regions. Furthermore, a modified adaptive parameter adjustment scheme is designed for individuals in each triple by considering their differences so as to meet the expectation that better individuals focus on exploitation while worse individuals concentrate on exploration. Finally, experiments are performed to first compare TCDE with totally 10 advanced DE variants and then further compare it with totally 10 CEC winners and their latest variants on the CEC'2014 and the CEC'2017 problem suites with totally 4 different dimensionality settings. Experimental results prove that TCDE achieves highly competitive or even much better performance than the totally 20 compared methods. Particularly, TCDE is demonstrated to be especially capable of solving complicated optimization problems. Furthermore, the efficacy of TCDE in tackling real-world optimization problems is substantiated through experiments conducted on the CEC'2011 real-world optimization problem set. [ABSTRACT FROM AUTHOR]

• A novel mutation mechanism named "DE/current-to-rwrand/1" is devised to evolve the population, so that a good compromise between high search diversity and fast search convergence can be maintained. • A non-linear selection probability is assigned to each individual, which is computed based on its function value ranking. • Better individuals preserve exponentially larger selection probabilities, while worse individuals have exponentially smaller chances to be selected as the guiding exemplars to direct the mutation of the population. • "DE/current-to-rand/1" and "DE/current-to-best/1" are two special cases of the designed "DE/current-to-rwrand/1". Differential evolution (DE) has been experimentally demonstrated to be effective in solving optimization problems. However, the effectiveness of DE encounters rapid deterioration in the face of complicated optimization problems with many grotesque local basins, which are emerging increasingly frequently nowadays. To alleviate this predicament, this paper devises a simple yet effective mutation scheme named "DE/current-to-rwrand/1" to further promote the optimization ability of DE in solving complicated optimization problems. Specifically, this strategy assigns a non-linear selection probability for each individual, which is computed based on its function value ranking. As a result, all individuals can be potentially selected to direct the mutation of the population, but better individuals preserve exponentially larger selection probabilities. In this way, the resultant DE, which is named function value ranking aware differential evolution (FVRADE), is expectedly capable of balancing high diversity and fast convergence of the population well to find satisfactory solutions to optimization problems. In particular, two classical and popular mutation strategies, namely "DE/current-to-rand/1" and "DE/current-to-best/1", are two special cases of the proposed mutation strategy. Abundant experiments have been extensively executed on the well-known CEC'2017 and the latest CEC'2021 benchmark problem sets. Experimental results have verified that FVRADE performs highly competitively with or even significantly better than several representative and state-of-the-art peer methods. In particular, it is experimentally demonstrated that FVRADE is particularly good at solving complicated optimization problems, and preserves a good scalability to deal with optimization problems. Besides, experiments have also been conducted on the popularly adopted CEC'2011 real-world optimization problem suite and the experimental results have substantiated that FVRADE is very promising to solve real-world optimization problems. [ABSTRACT FROM AUTHOR]

Optimization problems become increasingly complicated in the era of big data and Internet of Things, which significantly challenges the effectiveness and efficiency of existing optimization methods. To effectively solve this kind of problems, this paper puts forward a stochastic cognitive dominance leading particle swarm optimization algorithm (SCDLPSO). Specifically, for each particle, two personal cognitive best positions are first randomly selected from those of all particles. Then, only when the cognitive best position of the particle is dominated by at least one of the two selected ones, this particle is updated by cognitively learning from the better personal positions; otherwise, this particle is not updated and directly enters the next generation. With this stochastic cognitive dominance leading mechanism, it is expected that the learning diversity and the learning efficiency of particles in the proposed optimizer could be promoted, and thus the optimizer is expected to explore and exploit the solution space properly. At last, extensive experiments are conducted on a widely acknowledged benchmark problem set with different dimension sizes to evaluate the effectiveness of the proposed SCDLPSO. Experimental results demonstrate that the devised optimizer achieves highly competitive or even much better performance than several state-of-the-art PSO variants. [ABSTRACT FROM AUTHOR]

Hybridizing multiple mutation strategies has shown much effectiveness in helping differential evolution (DE) algorithms achieve good optimization performance. Though abundant adaptive ensemble strategies have been developed to adaptively employ multiple mutation strategies to evolve the population, most of them ignore to make full use of the properties and characteristics of the multiple mutation strategies. To fill this gap, this paper devises a bi-directional ensemble scheme for DE to adaptively assemble totally 8 mutation strategies with different properties and characteristics. As a result, a novel DE, which we call bi-directional ensemble DE (BDEDE), is developed. Specifically, this paper sorts the 8 mutation strategies roughly from two opposite perspectives, namely the convergence and the diversity. Then, we assign each mutation strategy with two different non-linear probabilities, which are calculated on the basis of its two rankings obtained from the two perspectives. Subsequently, to make full use of these mutation schemes, we first partition the whole population into two separate parts, namely elite individuals and non-elite individuals. Then, for each elite individual, we randomly select a mutation strategy from the 8 candidates based on the probabilities calculated by the convergence rankings, while for each non-elite individual, we stochastically choose a mutation scheme from the same 8 candidates but based on the probabilities computed by the diversity rankings. In this manner, the elite individuals prefer to exploit the located optimal areas, while the non-elite individuals tend to explore the solution space. Therefore, it is likely that BDEDE expectedly maintains a good balance between search diversity and search convergence. To further help BDEDE achieve such a purpose, this paper devises an adaptive partition strategy to dynamically separate the whole population into the two categories. With the above two techniques, BDEDE anticipatedly obtains good optimization performance. To verify its effectiveness and efficiency, we conduct experiments on the CEC2014 and the CEC2017 benchmark sets by comparing BDEDE with totally 14 well-known and state-of-the-art DE variants. Experimental results have shown that BDEDE performs competitively with or even significantly better than the 14 compared DE variants. The source code of BDEDE can be downloaded from https://gitee.com/mmmyq/BDEDE. [ABSTRACT FROM AUTHOR]